|
%I #12 Aug 02 2019 03:21:41
%S 5,266681,40799043101,86364397717734821,
%T 36190908596780862323291147613117849902036356128879432564211412588793094572280300268379995976006474252029,
%U 334279880945246012373031736295774418479420559664800307123320901500922509788908032831003901108510816091067151027837158805812525361841612048446489305085140033
%N Primes in A007406.
%C A007406 lists the Wolstenholme numbers.
%C Numbers k such that A007406(k) is prime are listed in A111354.
%H Carlos M. da Fonseca, M. Lawrence Glasser, Victor Kowalenko, <a href="https://doi.org/10.2298/AADM1801070F">Generalized cosecant numbers and trigonometric inverse power sums</a>, Applicable Analysis and Discrete Mathematics, Vol. 12, No. 1 (2018), 70-109.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HarmonicNumber.html">Harmonic Number</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WolstenholmesTheorem.html">Wolstenholme's Theorem</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WolstenholmeNumber.html">Wolstenholme Number</a>
%F a(n) = A007406(A111354(n)).
%e A007406 begins {1, 5, 49, 205, 5269, 5369, 266681, 1077749, 9778141, ...}.
%e Thus a(1) = 5 because A007406(2) = 5 is prime but A007406(1) = 1 is not prime.
%e a(2) = 266681 because A007406(7) = 266681 is prime but all A007406(k) are composite for 2 < k < 7.
%t Do[f=Numerator[Sum[1/i^2,{i,1,n}]]; If[PrimeQ[f],Print[{n,f}]],{n,1,250}]
%Y Cf. A111354, A007406, A001008, A007407, A067567, A056903.
%K nonn
%O 1,1
%A _Alexander Adamchuk_, Oct 11 2006
| 